The Impact of Aging, Dementia, and SES on Cognitive Decline
A Longitudinal Study Using Linear Mixed Models
Adasia M., Bess T., Preethi R.
Introduction
Linear Mixed Models (LMMs) are powerful statistical tools designed to analyze data with complex structures, such as hierarchical data (e.g., individuals within groups) or repeated measures (e.g., assessments taken over time). Unlike traditional methods, LMMs account for variations at both the group level and the individual level, making them ideal for studying patterns of cognitive decline across aging populations.
Why LMMs?
Fixed Effects: Capture overall population trends, like how age or socioeconomic status influences cognitive function on average.
Random Effects: Model differences between individuals, accounting for unique trajectories over time or variability across participants.
Data Flexibility: Handle missing data and unbalanced datasets effectively, ensuring reliable results even when some observations are incomplete.
Literature Review
Linear Mixed Models: An Overview
Extend simple linear regression by incorporating fixed effects (population-level) and random effects (subject-level variability).
Ideal for analyzing longitudinal and hierarchical datasets.
Provide unbiased estimates even with missing data (Bates, 2014; Gelman & Hill, 2007).
Covariance Structure
Essential for modeling dependencies between repeated measures (Starkweather, 2010).
Positive covariance: variables move together.
Negative covariance: variables move in opposite directions.
Allows explicit modeling of within-subject variability, critical for longitudinal studies.
Literature Review Continued
Robust Estimation
Methods that minimize the influence of outliers, ensuring parameter reliability (Agostinelli & Yohai, 2016).
Non-robust techniques like OLS regression are highly sensitive to extreme values and may yield biased results.
Challenges of Traditional Methods
Traditional linear models assume independence of observations, often violated in clustered data (Barr et al., 2013).
Handling missing data through listwise deletion or imputation can introduce bias (Enders, 2010).
Methods
Our Focus
This project applies LMMs to investigate:
The influence of age, dementia status, and socioeconomic factors on cognitive decline.
Cognitive function measured using the Mini-Mental State Examination (MMSE), a widely-used tool for assessing cognitive impairment.
How repeated assessments over time help us understand individual changes in cognitive function while capturing broader population trends.
Methods
Dataset: OASIS-Longitudinal MRI Data in Nondemented and Demented Older Adults
data <-read.csv("C:/IDC6940/IDC6940_BDP/oasis_longitudinal.csv")library(mice)imputed_data <-mice(data, m =5, method ='pmm')
iter imp variable
1 1 SES MMSE
1 2 SES MMSE
1 3 SES MMSE
1 4 SES MMSE
1 5 SES MMSE
2 1 SES MMSE
2 2 SES MMSE
2 3 SES MMSE
2 4 SES MMSE
2 5 SES MMSE
3 1 SES MMSE
3 2 SES MMSE
3 3 SES MMSE
3 4 SES MMSE
3 5 SES MMSE
4 1 SES MMSE
4 2 SES MMSE
4 3 SES MMSE
4 4 SES MMSE
4 5 SES MMSE
5 1 SES MMSE
5 2 SES MMSE
5 3 SES MMSE
5 4 SES MMSE
5 5 SES MMSE
Age Coefficient: -0.031 (small, non-significant decline with age).
Key Findings
Age alone is not a significant predictor of MMSE scores.
Indicates additional variables may explain cognitive decline.
Model 0: Age as the Sole Predictor
R Code
# Model 0: Age as the sole predictorlibrary("lme4")library("mitml")library("Matrix")model0 <-lapply(imputed_list, function(data) lmer(MMSE ~ Age + (1| Subject.ID), data = data))pooled_results <-testEstimates(model0, method ="D2")summary(pooled_results)
Call:
testEstimates(model = model0, method = "D2")
Final parameter estimates and inferences obtained from 5 imputed data sets.
Estimate Std.Error t.value df P(>|t|) RIV FMI
(Intercept) 29.718 2.454 12.112 48917.049 0.000 0.009 0.009
Age -0.033 0.032 -1.034 39962.092 0.301 0.010 0.010
Unadjusted hypothesis test as appropriate in larger samples.
Results: The age effect on MMSE was small and non-significant, suggesting that age alone does not fully explain cognitive decline.
Model 1: Adding Dementia Severity and SES
Examine the combined effect of age, dementia severity (CDR), and SES
Age and SES are not significant predictors in this model.
Model 1: Adding Dementia Severity and SES
R Code
model1 <-lapply(imputed_list, function(data) {lmer(MMSE ~ Age * Group + SES + (1| Subject.ID), data = data)})pooled_results <-testEstimates(model1, method ="D2")summary(pooled_results)
Call:
testEstimates(model = model1, method = "D2")
Final parameter estimates and inferences obtained from 5 imputed data sets.
Estimate Std.Error t.value df P(>|t|) RIV FMI
(Intercept) 34.551 6.459 5.349 2.606e+05 0.000 0.004 0.004
Age -0.069 0.081 -0.855 2.834e+06 0.392 0.001 0.001
GroupDemented -4.465 7.265 -0.615 5.642e+05 0.539 0.003 0.003
GroupNondemented -4.165 6.933 -0.601 8.978e+06 0.548 0.001 0.001
SES -0.272 0.216 -1.260 6.970e+01 0.212 0.315 0.260
Age:GroupDemented 0.007 0.092 0.078 2.177e+05 0.938 0.004 0.004
Age:GroupNondemented 0.062 0.087 0.708 3.153e+06 0.479 0.001 0.001
Unadjusted hypothesis test as appropriate in larger samples.
Results: This model showed no significant effects for age, SES, or age-by-group interactions, indicating that additional factors may better explain cognitive decline.
Call:
testEstimates(model = final_model, method = "D2")
Final parameter estimates and inferences obtained from 5 imputed data sets.
Estimate Std.Error t.value df P(>|t|) RIV FMI
(Intercept) 17.621 3.608 4.884 3.284e+06 0.000 0.001 0.001
CDR -5.230 0.456 -11.474 1.787e+04 0.000 0.015 0.015
nWBV 15.349 4.873 3.150 3.891e+06 0.002 0.001 0.001
Unadjusted hypothesis test as appropriate in larger samples.
Results: CDR was significantly associated with MMSE scores, showing that higher dementia severity leads to lower cognitive function. Additionally, higher nWBV was associated with higher MMSE, supporting its role in cognitive preservation.
Conclusions
Key Takeaways
Age alone does not predict cognitive decline.
Dementia severity (CDR) is a strong negative predictor.
Higher brain volumes (nWBV) are protective against cognitive decline.
References
Agostinelli, C., & Yohai, V. J. (2016). Composite robust estimators for linear mixed models. Journal of the American Statistical Association, 111(516), 1764-1774. https://doi.org/10.1080/01621459.2015.1115358
Bates, D. (2014). Fitting linear mixed-effects models using lme4. arXiv preprint arXiv:1406.5823.
Baayen, R. H., Davidson, D. J., & Bates, D. M. (2008). Mixed-effects modeling with crossed random effects for subjects and items. Journal of Memory and Language, 59(4), 390-412.
Barr, D. J., Levy, R., Scheepers, C., & Tily, H. J. (2013). Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of Memory and Language, 68(3), 255-278.